Long- and short-range structures of Ti1-xHfxNi1.0/1.1Sn half-Heusler compounds and their electric transport properties

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Long- and short-range structures of Ti_1−xHf_xNi1.0/1.1Sn half-Heusler compounds and their electric transport properties

Matylda N. Guzik, Matthias Schrade, Raluca Tofan, Patricia A. Carvalho, Kristian Berland, Magnus H. Sørby, Clas Persson, Anette E. Gunnæs and Bjørn C. Hauback Experimental study reveals the apparent ordered arrangement of excess Ni at the nominally vacant sublattice in thermoelectric Ti1−xHf_xNi1.0/1.1Sn half-Heusler compounds.

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Matylda N. Guzik 0000-0001-6349-4659

Matthias Schrade 0000-0002-9501-6536

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Patricia A. Carvalho

Kristian Berland

Magnus H. Sørby

Clas Persson

Anette E. Gunnæs

Bjørn C. Hauback

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Journal:CrystEngComm Paper:c9ce00046a

Title:Long- and short-range structures of Ti1−xHf_xNi1.0/1.1Sn half-Heusler compounds and their electric trans- port properties

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CrystEngComm

PAPER

Cite this: DOI:10.1039/c9ce00046a

Received 9th January 2019, Accepted 4th May 2019 DOI: 10.1039/c9ce00046a rsc.li/crystengcomm

Long- and short-range structures of Ti

Hf

Ni

Sn half-Heusler compounds and their electric transport properties †

Q1

Q2 Matylda N. Guzik, ‡^abMatthias Schrade, ^bRaluca Tofan,^bPatricia A. Carvalho,^c Kristian Berland,^bdMagnus H. Sørby,^aClas Persson,^b

Anette E. Gunnæs^band Bjørn C. Hauback^a

A commercially feasible, nontoxic material that would convert heat into electricity in an efficient and cheap way has not yet been identified. Half-Heusler compounds are one the most interesting candidates but to become competitive their thermoelectric properties still need to be improved. Atomic substitution and ex- cess Ni in the crystal structure of ternary MNiSn half-Heuslers are among the most successful approaches used to boost their performance. Here, we report on the effect of both methods applied simultaneously to the series of polycrystalline Ti_1−xHf_xNi1.0/1.1Sn,x= 0.00, 0.10, 0.15, 0.20, samples. High-resolution synchro- tron powder X-ray diffraction studies combined with transmission electron microscopy demonstrate the crystallization of single or multiple Hf-substituted half-Heusler phase(s). The analysis of their long-range atomic structures shows that most of them contain interstitial Ni atoms disorderly distributed at the nomi- nally vacant 4d sites. However, the short-range atomic correlations suggest that, for some compositions, excess Ni creates an orderly arranged additional atomic plane at the vacant fcc sublattice, which can be seen as a defective half- and/or full-Heusler phase. The results also show that the Ni-rich samples crystal- lize with the micrometer-sized full-Heusler phases, while all Hf-incorporating compositions present disper- sion of HfO2nanoprecipitates in the grains of the half-Heusler matrix. This research is complemented by thermoelectric transport measurements of the studied compositions in the range of 300–750 K. The results suggest that neither Seebeck coefficient nor electrical resistivity shows an obvious correlation with the ob- served microstructures. These finding are discussed with respect to previously proposed transport mechanisms.

Introduction

A good thermoelectric (TE) material is defined by high energy conversion efficiency, light weight, good chemical and me- chanical stability, low-toxicity and an affordable price.¹ Half- Heusler (HH) compounds potentially satisfy all above condi- tions and for this reason have been extensively investigated

over the last two decades.² These cost-effective materials, consisting of environmental friendly and abundant elements, are chemically stable in the medium to high temperature range (600–1100 K).^3–5 However, the HHs still present chal- lenges that must be addressed before they can be effectively implemented in technological applications. One of the main obstacles is their high thermal conductivity as compared to current alternatives.^5,6Thus, to enhance the TE performance of HHs, various synthesis and processing methods, modifying chemistry and microstructure (e.g. atomic substitution, dop- ing, nanostructuring), have been applied separately or jointly.^4,5,7,8 Although, the advances achieved so far demon- strate that their TE properties can be significantly improved, our understanding of key factors that govern the TE efficiency of HHs is still limited. This is mostly due to the strong re- search focus on thermal and electric transport properties of this family of compounds and less attention to their struc- tural characterization. In addition, there is large variation in the data reported for nominally identical HH compositions, prepared by either the same or different synthesis methods.

aPhysics Department, Institute for Energy Technology, P.O. Box 40, N-2027 Kjeller, Norway

bDepartment of Physics, Centre for Materials Science and Nanotechnology, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway

cSINTEF Materials and Chemistry, P.O. Box 124 Blindern, N-0314 Oslo, Norway

dFaculty of Science and Technology, Norwegian University of Life Sciences, P.O.

Box 5003 NMBU, N-1432 Ås, Norway

†Electronic supplementary information (ESI) available: 1) Graphical representa- tion of Rietveld refinement results for all studied compositions, 2) STEM images with formed phases/nanoprecipitates in the investigated materials, 3) plots ofS andρvs.occupancy of the 4d site, abundance of FH and HfO2in studied sam- ples. See DOI: 10.1039/c9ce00046a

‡The main author is currently working at the Department of Technology Sys- tems of the University of Oslo. E-mail: [email protected].

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2 | CrystEngComm, 2019,00, 1–13 This journal is © The Royal Society of Chemistry 2019 From this perspective, insight into the relationship between

structural and TE properties of both already studied and yet unexplored HH compositions is needed to accelerate progress in the field.

N-type HHs, with the general chemical formulaABC(A,B- transition metal atom, C-main group element), crystallize with a cubic symmetry (F4¯3m). Their crystal structure can be perceived as an interpenetration of four face-centered cubic (fcc) lattices with four characteristic crystallographic sites in the unit cell: 4a (0, 0, 0) occupied byA, 4c (1/4, 1/4, 1/4) occu- pied byB, 4b (1/2, 1/2, 1/2) occupied by Catoms and the ad- ditional nominally unfilled tetrahedral 4d site (3/4, 3/4, 3/4).

Ti-Rich Ti_1−xMxNiSn (M = Hf, Zr), as the lightest and cheapest among other n-type HHs, should be of great interest for prac- tical applications, however, their relatively poor thermoelec- tric performance make them less attractive than other HH compositions.^9–11Although, structural studies of TiNiSn and Ni-rich TiNi1+xSn compounds, based on powder X-ray and neutron diffraction (PXD and PND, respectively) as well as scanning transmission electron microscopy (STEM) are quite vast,^4,6,12–21 there is a limited number of reports on substituted Ti_1−xMxNiSn in the Ti-rich region.^22–26 Consider- ing that: i) understanding of the crystal structure is crucial for optimization of thermoelectric performance, and ii) Ti- and Ni-rich (Ti,Hf)NiSn phases are among the least-studied compositions, we have in this work synthesized and performed a comprehensive structural characterization of n-type compounds with the general formula Ti_1−xHfxNiySn,x

= 0.00, 0.10, 0.15, 0.20 andy= 1.0, 1.1. Our previous investi- gation showed that high-quality diffraction data, in particular high-resolution, are indispensable for reliable crystallo- graphic analysis of HH phases.²⁷Thus, in the present study, all samples were examined by high-resolution synchrotron ra- diation powder X-ray diffraction (SR-PXD).

The reported PXD data for arc-melted and annealed (1073 K) Ti_1−xHfxNiSn, x = 0.00, 0.05, 0.10, 0.20, 0.30, 0.40, 0.50, showed formation of the HH phase but also small amounts of FH and Sn5Ti6.²²Samples with x= 0.10 and 0.20 demon- strated reduced Seebeck coefficient (S) and the electrical con- ductivity (σ), in the range of 300–950 K. Higher Hf concentra- tion (x= 0.30–0.50) increased the values of both parameters.

The overall increase of the TE performance was explained by the Hf-induced reduction of the lattice thermal conductivity with no clarification of changes observed in the electric trans- port properties. Data for Ti0.95Hf0.05NiSn and Ti0.2Hf0.8NiSn,²³ prepared by arc melting/spark plasma sintering and annealing at 1073 K, showed reduced electrical resistivity (ρ= σ⁻¹) in comparison to pure TiNiSn. The Hf presence de- creased the Seebeck coefficient in both samples, however, much lower|S|was observed for Ti0.2Hf0.8NiSn, indicating a higher intrinsic carrier concentration.²³As expected, the ther- mal conductivity (κ) of both materials was also lower than that of TiNiSn. In other studies, Ti_1−xHfxNiSn, x = 0.25 and 0.50, were characterized by higher electrical resistivity than TiNiSn, however its lower value was observed in a sample with the higher Hf amount.²⁴Interestingly, changes inSvar-

ied. While for Ti0.75Hf0.25NiSn, the observed|S| were higher than for TiNiSn in the range of 300–850 K, for Ti0.5Hf0.5NiSn, S increased only slightly between 550 K and 700 K, suggesting a similar intrinsic carrier concentration. Hf substi- tution also loweredκ, which was similar in both samples. Re- cently, a Ti_1−xHfxNiSn_1−ySby sample series prepared by low-/

high-temperature rapid solidification and spark plasma sintering, was investigated by PXD and STEM.²⁵ Diffraction data reported for as-solidified Ti_1−xHfxNiSn,x= 0.0, 0.2, 0.3, 0.4, 0.5, showed the presence of the HH phase in both low- and high-temperature processed powders. Additionally, FH, Sn5Ti6and metallic Sn were detected. The sample phase com- positions changed upon densification, resulting in formation of the phase-pure HH materials, in the low-temperature solid- ified powders. However, PXD measurements were carried out with a laboratory diffraction instrument (λ = Cu Kα), which due to possibly limited-resolution²⁷may have generated data with insufficient quality for reliable phase analysis. STEM in- vestigation of the local disorder in the same sample series showed fluctuation in the HH chemical composition, signal- ing a possible phase separation. These studies did not report nucleation of FH precipitates but demonstrated formation of the large local lattice strain originating from the presence of disorderly distributed Ni atoms, which induced (Ti,Hf)/Sn anti-site defects.²⁵

In the research reported on the TiNiSn-based HH systems, the amount of Ni has been shown to affect the electric trans- port properties and, at the same time, reduce of the lattice thermal conductivity in the HH compounds.^9,10,14,19 Studies performed so far indicate that excess Ni either statistically oc- cupies an available subset of tetrahedral interstitial sites (4d) in the HH structure and/or becomes a nucleation center of the full-Heusler phase(s).14,15,19,28–31 In this work, through comprehensive investigation of long- and short-range atomic structures of the Ti_1−xHfxNiySn HH phases, x = 0.00, 0.10, 0.15, 0.20 and y = 1.0, 1.1, we address three questions: 1) what is the nature of Hf-/Ni-related processes in the selected HH compounds, 2) what is the correlation between a long- range atomic order and a local atomic structure in HH phases, and 3) what is the relationship between the crystal chemistry/microstructure and electric transport properties of chosen compositions.

Experimental details

Synthesis and processing of materials

Two series of polycrystalline samples, with the following nomi- nal compositions: Ti_1−xHfxNiSn and Ti_1−xHfxNi1.1Sn,x = 0.00, 0.10, 0.015, 0.20, were synthesized. Metallic pieces (Ti, Hf, Ni, Sn: Goodfellow, purity>99.5%) were first arc melted under Ar atmosphere, in a water-cooled cooper heart with a tungsten electrode. To improve sample homogeneity pellets were flipped and remelted several times. The obtained ingots were ball milled with an 8000D SPEX mixer for 6 minutes, at constant ve- locity of ca. 1000 rpm. Mechanochemical powder processing was carried out in stainless steel vials, with a ball-to-powder CrystEngComm Paper

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weight ratio of 3 : 1. The resulting fine-grained powders were cold pressed into pellets, wrapped in Ta foil and subsequently sealed under Ar atmosphere in stainless steel tubes. The sam- ples were then annealed at 950°C for one week and eventually water quenched. Prior to characterization, the pellets were cut into smaller pieces with a diamond saw.

Characterization methods

High-resolution SR-PXD measurements of both as-cast and heat-treated materials were carried out at the Swiss- Norwegian Beamline, ESRF, Grenoble (France). Data were col- lected at the BM31 station, equipped with a high-resolution powder X-ray diffraction instrument (λ = 0.50218 Å, 2θ= 1– 40°, point detector with analyzer crystals). The samples were crushed with a mortar to a fine powder and loaded in sealed 0.3 mm diameter boron-glass capillaries, which were rotated during measurements to improve powder averaging. The col- lected data were analyzed by Rietveld refinements using the Fullprof Suite program.³² The analysis of Bragg scattering provided exhaustive information on the long-range order of the HH atomic structure, represented by the unit cell (i.e.the time- and space-averaged position of atoms). The diffraction profiles were modelled with a pseudo-Voigt peak shape func- tion and the background was defined by interpolation be- tween manually chosen points. The SR-PXD data of the Ti_1−xHfxNiSn sample series were fitted against the Ni-rich model of the HH phase, which represented an averaged atomic arrangement within the HH matrix and included oc- cupancy of the nominally unfilled 4d crystallographic posi- tion. Rietveld refinements of the SR-PXD patterns for the Ti_1−xHfxNi1.1Sn sample series were performed with an addi- tional model of the FH crystal structure with an independent lattice parameter. For the identified HH/FH phase(s), the fol- lowing parameters were allowed to vary during the refine- ment cycles: a scale factor, up to six profile parameters (U,V, W, mixing factor and two asymmetry parameters), a unit cell parameter, overall or individual displacement parameters, an occupancy factor for 4a, 4c/8c and 4d sites. Due to a high number of phases and/or poor crystallinity of the as-cast pow- ders, the occupancy of the 4d interstice in the HH structure was refined only for the annealed samples. All data were corrected for X-ray absorption, which was calculated assum- ing a packing fraction of 0.5 in the capillaries.

The microstructure and chemical composition in the se- lected samples of the annealed Ti_1−xHfxNiSn series were char- acterized by transmission electron microscopy (TEM) and an- nular bright field (ABF)/high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) coupled to X-ray energy dispersive spectroscopy (EDS). As SR- PXD did not provide any information about short-ranged structural features, TEM was also applied to investigate a lo- cal atomic arrangement (i.e. a short-range atomic structure) in the chosen materials. This work was performed with a DCOR Cs probe-corrected FEI Titan G2 60-300 instrument, with 0.08 nm nominal spatial resolution when operated at

300 kV, equipped with a Bruker SuperX EDS system compris- ing four silicon drift detectors. TEM sample preparation in- volved depositing powder suspended in isopropanol on lacey carbon grids followed by shielded plasma cleaning. The local crystal structure and lattice strain were analyzed by performing fast Fourier transform (FFT) with the DiffTools³³ and geometric phase analysis (GPA) script packages, devel- oped for Digital Micrograph (Gatan Inc).

The in-plane Seebeck coefficient and electrical resistivity were measured under Ar atmosphere using a custom made set- up.³⁴Each sample was measured over up to six heating–cooling cycles and pellets were not polished in between. In Fig. 8 only one full cycle is displayed for clarity, as no significant changes in the electric transport properties were observed. The thermal conductivity was not measured here, as the samples were only compacted by cold-pressing of powders, followed by conven- tional sintering, and were likely to deviate in their relative den- sity, thus preventing a meaningful comparison.

Ab initiocalculations

Density functional theory (DFT) was used to calculate the mixing energy of Ti_1−xHfxNiySn as a function ofy, for selected

Fig. 1 High-resolution SR-PXD profiles (λ = 0.50218 Å) for the arc melted (a) and annealed (b) Ti_1−xHf_xNi1.0/1.1Sn powders.

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4 | CrystEngComm, 2019,00, 1–13 This journal is © The Royal Society of Chemistry 2019 xvalues. A supercell approach was employed with the Vienna

ab initio simulation package (VASP), a projector-augmented plane-wave code, with the Perdew–Burke–Ernzerhof (PBE) ex- change–correlation function.^35,36The recommended Ni maxi- mum energy cutoff of 270 eV was utilized^35,36and the struc- ture was relaxed until interatomic forces became smaller than 0.02 eV Å⁻¹. For each composition, five 2×2×2 conven- tional unit cells were generated with a pseudo-random distri- bution of Hf/Ti substitutions and Ni interstitials. Semi- uniformity was imposed, by considering only subcell, where the number of Ni and Hf within each of 1 ×1 × 1 subcells could differ by no more than 1. For a given composition, only the supercell with the lowest mixing energy was retained.

Results and discussion

High-resolution synchrotron powder X-ray diffraction (SR- PXD) study

Ti_1−xHf_xNi_ySn as-cast samples.The high number of identi- fied phases and poor crystallinity of the as-cast powders lim- ited number of refined parameters during the Rietveld analy- sis (Table 1 and ESI†). Thus, as already mentioned in section Experimental details, the obtained compositional and struc- tural information is only partial. Due to that, numbers listed in Table 1 represent a trend among identified phases in stud- ied compositions and should not be treated as absolute values. The SR-PXD data of the arc melted TiNiSn and TiNi1.1- Sn show the formation of HH, FH, binary Sn5Ti6, Sn3Ti5and metallic Sn (Fig. 1a, Table 1 and ESI†). The refined value of the HH unit cell parameter in TiNi1.1Sn, a = 5.9504(1) Å, is slightly larger than in TiNiSn,a= 5.9484(2) Å, and both are significantly enlarged compared to the same phase present in the already reported annealed and/or hot-pressed/spark plasma sintered materials (∼5.93 Å).4,6,13,14,16–19,24,37 This is likely due to the higher degree of intrinsic disorder in their crystal structures, as commonly observed for phases formed in rapidly cooled/solidified powders. The FH lattice constant is identical in both samples,a= 6.0599(2) and 6.0596(2) Å for TiNiSn and TiNi1.1Sn, respectively, and smaller than values reported for the annealed TiNi2Sn (a= 6.095(3) Å).³⁸The Hf- containing samples crystallize with the same compounds as TiNi1.0/1.1Sn, but a second HH phase is formed in addition.

The observed phase compositions are in agreement with the theoretical predictions for the Ti_1−xHfxNiSn system³⁹and with the experimental results published for arc melted samples with the same compositions.^13,22,40The unit cell parameters of Ti_1−xHfxNiSn HHs formed in each sample differ slightly, which results from small deviations in their chemical compo- sitions. Both phases are Ti-rich, but one of them has a higher amount of Ti (hereafter referred to as HH1 or Ti-enriched) than the other (hereafter referred to as HH2 or Hf-enriched).

Interestingly, the HH phases formed in both investigated se- ries exhibit almost the same Ti/Hf fraction at 4a sites (Table 1). The increasing amount of Hf reduces the occu- pancy of the 4a site by Ti in both HH structures (Table 1), and in turn, expands their unit cells. The results also demon-

strate incorporation of Hf into the FH structure but show that increasing Hf content decreases the FH concentration in both sample series. A summary of the Rietveld refinement re- sults is presented in Table 1.

Ti_1−xHf_xNi_ySn annealed samples. High-resolution SR-PXD data for the annealed Ti_1−xHfxNi1.0/1.1Sn materials indicate a tremendous change of the phase abundance in both sample se- ries (Fig. 1–3, Table 2 and ESI†). Powder patterns of TiNiSn and Ti0.9Hf0.1NiSn are indexed with a single HH phase that ac- counts for 95.2 and 95.4% of the sample mass, respectively.

Apart from that, only small amounts of metallic Sn and HfO2

are present in the samples (Table 2). The latter appears to form easily and has already been reported in Hf-based MNiSn pow- ders.^17,27The corresponding Ni-rich compositions tend to addi- tionally form an ordered FH phase, whose fraction is highest in the Hf-free TiNi1.1Sn (9.8 vs.6.8 wt% in Ti0.9Hf0.1Ni1.1Sn). Its occurrence lowers the concentration of HH in both TiNi1.1Sn and Ti0.9Hf0.1Ni1.1Sn (89.7 and 91.5 wt%, respectively). The HH lattice constant in TiNiSn and TiNi1.1Sn is 5.93419(3) and 5.94226(3) Å, respectively. The slightly largeravalue of the lat- ter is likely to result from a higher degree of disorder in the crystal structure caused by the excess Ni. In both HHs, Ni oc- cupies orderly the 4c site but its presence at 4d varies and cor- responds to 5% and 8% in TiNiSn and TiNi1.1Sn, respectively (Fig. 3 and Table 2). Theavalues as well as the fractions of dis- ordered Ni atoms are in agreement with previous reports for nominally identical samples.12,15,16,18,19

The HH phases formed in Ti0.9Hf0.1NiSn and Ti0.9Hf0.1Ni1.1Sn have similar averaged chemical compositions refined to Ti0.906Hf0.094NiSn and Ti0.925Hf0.075Ni1.09Sn, respec- tively (Fig. 2 and Table 2). Interestingly, Rietveld analysis does not suggest any extra Ni in the HH structure in the nominally stoichiometric sample. However, in Ti0.925Hf0.075- Ni1.09Sn, 9% of the 4d site is occupied by disorderly distrib- uted Ni atoms. This could be a reason of the larger lattice constant obtained for this phase (a= 5.95402(6) Å), as com- pared to Ti0.906Hf0.094NiSn (a = 5.94192(6) Å), despite a slightly lower fraction of Hf in the structure (Fig. 3). The FH phase formed in Ti0.9Hf0.1Ni1.1Sn does not show any Ni defi- ciency, as previously reported by Downieet al.¹⁹

SR-PXD patterns for Ti0.85Hf0.15Ni1.0/1.1Sn and Ti0.8Hf0.2- Ni1.0/1.1Sn suggest that two Ti-rich HH phases (HH1 and HH2, see section Ti_1−xHfxNiySn as-cast samples) and a small amount of HfO2are formed in both samples. The Ni-rich ma- terials crystallize with an additional FH phase, while in the Ni-stoichiometric series, metallic Sn is observed in addition to the HH phases. HHs formed in corresponding samples of both series reveal similar refined compositions (see Table 2).

An increasing amount of Hf reduces the number of Ti at the 4a site in the HH crystal structures but does not affect signifi- cantly the FH fraction formed in the Ni-rich samples. In Ti0.85Hf0.15NiSn, the small difference in lattice constants be- tween HH1 and HH2 (a= 5.94969(8) Åvs.5.9647IJ1) Å, respec- tively) can be attributed to the variation in the Hf/Ti ratio.

The Rietveld refinements demonstrate that, while the 4c site is fully occupied by Ni atoms in both phases, the 4d position CrystEngComm Paper

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Table1Latticeparameter(a),phaseabundance,fractionaloccupancies(n),displacementparameters(Biso/Biso_overall)andgoodness-of-fit(χ2)valuesfortheTi1−xHfxNiySnHHandFHphasesintheas- castsamplesobtainedbyRietveldanalysisofhigh-resolutionSR-PXDdata.Estimatedstandarddeviationsaregiveninparentheses As-castTiNiSnTiNi1.1SnTi0.9Hf0.1NiSnTi0.9Hf0.1Ni1.1SnTi0.85Hf0.15NiSnTi0.85Hf0.15Ni1.1SnTi0.8Hf0.2NiSnTi0.8Hf0.2Ni1.1Sn HH1[wt%]48(1)43(1)37.6(6)35(1)36(1)34(1)36(1)42(1) a[Å]5.9484(2)5.9504(1)5.9666(3)5.9705(4)5.9750(4)5.9758(5)5.9818(6)5.9850(7) RefinedcompositionTiNi0.948SnTiNi0.938SnTi0.895Hf0.105NiSnTi0.885Hf0.115NiSnTi0.840Hf0.160NiSnTi0.850Hf0.150NiSnTi0.803Hf0.197NiSnTi0.803Hf0.197NiSn Atom(n) Ti(4a)1.00IJ−)1.00IJ−)0.895(3)0.885(5)0.840(1)0.850(5)0.803(5)0.803(5) Hf(4a)0.00IJ−)0.00IJ−)0.105IJ−)0.115IJ−)0.160IJ−)0.150(5)0.197IJ−)0.197IJ−) Sn(4b)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−) Ni(4c)0.948(8)0.938(8)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−) Biso_overall[Å2 ]0.61(3)0.77(1)0.12(4)0.12(6)0.03(5)0.12(5)0.16(5)0.11(4) HH2[wt%]——15.5(6)15(1)29(1)25(1)34(1)20(1) a[Å]——6.0033(3)6.0039(4)6.0156(3)6.0145(4)6.0231(3)6.0210(3) Refinedcomposition——Ti0.81Hf0.19NiSnTi0.83Hf0.17NiSnTi0.718Hf0.282NiSnTi0.738Hf0.262NiSnTi0.61Hf0.39NiSnTi0.64Hf0.36NiSn Atom(n) Ti(4a)——0.81(1)0.83(1)0.718(8)0.738(8)0.61(1)0.64(2) Hf(4a)——0.19IJ−)0.17(−)0.282IJ−)0.262IJ−)0.39IJ−)0.36IJ−) Sn(4b)——1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−) Ni(4c)——1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−) Biso_overall[Å2]——1.1(1)1.2(2)0.66(7)1.0(1)0.70(6)1.0(1) FH1[wt%]36(1)41(1)26.9(5)36.2(8)15.6(5)26.6(6)14.5(5)25.1(6) a[Å]6.0599(2)6.0596(1)6.0776(3)6.0814(3)6.0906(6)6.0886(5)6.0942(7)6.0929(5) RefinedcompositionTiNi2SnTiNi2SnTi0.855Hf0.145Ni2SnTi0.850Hf0.150Ni2SnTi0.80Hf0.20Ni2SnTi0.783Hf0.217Ni2SnTi0.76Hf0.24Ni2SnTi0.755Hf0.245Ni2Sn Atom(n) Ti(4a)1.00IJ−)1.00IJ−)0.855(5)0.850(1)0.80(1)0.783(8)0.76(2)0.755(8) Hf(4a)0.00IJ−)0.00IJ−)0.145IJ−)0.150IJ−)0.20(1)0.217IJ−)0.24(2)0.245IJ−) Sn(4b)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−) Ni(8c)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−)1.00IJ−) Biso_overall[Å2]1.07(4)1.01(4)0.62(6)0.83(5)0.66(9)0.63(6)0.7(1)0.41(6) Sn[wt%]3.1(1)2.0(1)3.3(1)2.3(1)3.4(2)2.1(2)3.4(2)2.0(1) Sn5Ti6[wt%]6.6(3)8.5(4)8.5(4)6.0(4)8.0(6)6.1(6)4.7(8)6.3(7) Sn3Ti5[wt%]6.3(3)5.5(3)8.2(4)5.5(3)8.0(4)6.2(5)7.4(5)4.5(4) χ22.672.062.943.192.842.502.992.45

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6 | CrystEngComm, 2019,00, 1–13 This journal is © The Royal Society of Chemistry 2019 is filled to much lesser extent. Only 4% and 1% of the site is

disorderly populated by Ni in the crystal structure of HH1 and HH2, respectively (Table 2 and Fig. 3).

In nominal Ti0.85Hf0.15Ni1.1Sn, 7.4 wt% of FH is formed at the expense of the Hf-enriched HH2 (14 wt%). Its presence in- creases the amount of HH1 by 6 wt% and rises the fraction of interstitial Ni from 4% to 10%, compared to Ti0.85Hf0.15NiSn.

While the unit cell parameters of HH2 (Table 2) are almost the same in Ti0.85Hf0.15NiSn and Ti0.85Hf0.15Ni1.1Sn, theavalue for HH1 in the Ni-rich composition is somewhat larger. This could result from a slightly higher Hf and/or extra interstitial Ni frac- tion in the crystal structure.

The abundance of phases in nominal Ti0.8Hf0.2NiSn is com- parable to that of Ti0.85Hf0.15NiSn, with a small increase in HH2, which takes place at the expense of HH1 (Table 2). The reduced amount of Ti in both structures leads to an expansion of their unit cells (a= 5.95511(8) and 5.9738(1) Å for HH1 and HH2, respectively). The higher amount of Hf in HH1 raises the fraction of interstitial Ni populating the 4d site, as compared to HH1 of Ti0.85Hf0.15NiSn. However, it does not affect the occu- pancy of this site in HH2. Though, the phase composition of Ti0.8Hf0.2Ni1.1Sn is the same as of Ti0.85Hf0.15Ni1.1Sn, the frac- tion of compounds present varies (Table 2). The FH phase crys- tallizes at the cost of Ti-enriched HH1 and its amount is higher than in Ti0.85Hf0.15Ni1.1Sn. At the same time, in the Ni-rich Ti0.8Hf0.2Ni1.1Sn the fraction of Ti-enriched HH1 and amount of extra Ni at the 4d site is higher than in Ti0.8Hf0.2NiSn.

The obtained results suggest that the single, thermody- namically stable Ti_1−xHfxNiySn HH phase crystallizes exclu- sively in samples with the following nominal compositions:

TiNiSn/TiNi1.1Sn and Ti0.9Hf0.1NiSn/Ti0.9Hf0.1Ni1.1Sn. The solu- bility limit of Hf in TiNiSn and TiNi1.1Sn is not affected by the Ni amount. The experimental range of the Ti_1−xHfxNi1.0/1.1Sn solid solution in the Ti-rich system is 0<x<0.15 at 1223 K and appears more restricted than the solubility regions suggested earlier by empirical (Ti0.74Hf0.26NiSn at 1273 K)^37,41

and theoretical studies (Ti0.83Hf0.17NiSn at 1273 K,³⁹miscibil- ity over the whole composition range at 500 K (ref. 42) or 700 K (ref. 43)). For samples withx≥0.15, formation of two Hf- incorporating HH phases is observed. Both compounds are Ti-rich and separation into more abundant Ti-enriched (HH1) and less abundant Hf-enriched (HH2) compositions is ob- served. In the Ti_1−xHfxNiSn samples, excess Ni is associated exclusively with the HH phase as no FH is formed. Ni atoms are distributed disorderly at the nominally vacant 4d site in the HH crystal structure. In the Ni-rich compositions, segrega- tion of the FH phase takes place. In Ti0.9Hf0.1Ni1.1Sn and Ti0.85Hf0.15Ni1.1Sn, FH accommodates less Ni (6.8 and 7.4%, respectively) than the 4d sites in the HH structures (∼9% oc- cupancy). However, in Ti0.8Hf0.2Ni1.1Sn the opposite trend is observed (8.7% of FH vs. 7.8% of Ni at the 4d site in HH).

Interestingly, in all Ti-enriched compositions, regardless of the nominal Ni amount, higher percentage of Ni occupies the 4d site (4–10%) than in Hf-enriched phases (0–4%). The pres- ence of Hf in the Ni-rich samples also hinders crystallization of the FH phase as compared to TiNi1.1Sn. The abundance of HfO2 in the Ti_1−xHfxNiSn sample series is rather constant, while its concentrations rises in Ti_1−xHfxNi1.1Sn as the Hf amount increases (1.7 wt% and 3.64 wt% in Ti0.9Hf0.1Ni1.1Sn and Ti0.8Hf0.2Ni1.1Sn, respectively). Metallic Sn, present only in the Ti_1−xHfxNiSn sample series, gradually disappears with a higher fraction of Hf in the sample (2.0 wt% and 0.67 wt% in Ti0.9Hf0.1NiSn and Ti0.8Hf0.2NiSn, respectively). Its concentra- tion in the TiNiSn and TiNi1.1Sn samples is the same and equals 0.45 wt%. A summary of the Rietveld refinements is presented in Table 2.

DFT calculations

The DFT calculations were performed to get a better insight into the observed preferential distribution of Ni atoms over compositionally different HH phases. The simulations Fig. 2 Observed (dots), calculated (line) and difference (bottom line) high-resolution SR-PXD patterns (λ= 0.50218 Å) obtained for annealed Ti0.9Hf0.1NiSn (a) and Ti0.9Hf0.1Ni1.1Sn (b). Vertical bars indicate Bragg peaks positions of contributing phases, from top to bottom: (a) HH, Sn, HfO2; (b) HH, FH, HfO2.

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